First slide

Position Path Length (Distance) And Displacement

Question

A particle located at x = 0, at time t = 0, starts moving along the positive X-direction with a velocity v that varies as $v = α \sqrt{x} .$ The displacement of the particle varies with time as

Easy

A

$t^{3}$
B

$t^{2}$
C

t
D

t^1/2

Solution

$\begin{aligned} v = α \sqrt{x} \\ v^{2} = α^{2} x \end{aligned}$
comparing $v^{2} = 2 ax$
$a = \frac{α^{2}}{2} = constant S \propto t^{2}$

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